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Nonparametric Empirical Bayes Estimation of the Matrix Parameter of the Wishart Distribution

โœ Scribed by Marianna Pensky

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
168 KB
Volume
69
Category
Article
ISSN
0047-259X

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โœฆ Synopsis

We consider independent pairs (X 1 , 7 1 ), (X 2 , 7 2 ), ..., (X n , 7 n ), where each 7 i is distributed according to some unknown density function g(7) and, given 7 i =7, X i has conditional density function q(x | 7) of the Wishart type. In each pair the first component is observable but the second is not. After the (n+1) th observation X n+1 is obtained, the objective is to estimate 7 n+1 corresponding to X n+1 . This estimator is called the empirical Bayes (EB) estimator of 7. An EB estimator of 7 is constructed without any parametric assumptions on g(7). Its posterior mean square risk is examined, and the estimator is demonstrated to be pointwise asymptotically optimal.

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